1. Field of the invention
The present invention relates to a light-emitting device having at least two pairs of a quantum-wave interference layer that effectively reflects carriers, or electrons and holes, respectively. In particular, the invention relates to light-emitting semiconductor devices including a laser (LD) and a light-emitting diode (LED) with improved luminous efficiency by effectively confining carriers with an active layer.
2. Description of the Related Art
An LD has been known to have a double hetero junction structure whose active layer is formed between n-type and p-type cladding layers. The cladding layers function as potential barriers for effectively confining carriers, or electrons and holes, within the active layer.
However, a problem persists in luminous efficiency. Carriers overflow the potential barriers of the cladding layers, which lowers luminous efficiency. Therefore, further improvement has been required, as presently appreciated by the present inventors.
As a countermeasure, forming cladding layers with a multi-quantum well structure of a first and a second layers as a unit to reflect carriers has been suggested by Takagi et al. (Japanese Journal of Applied Physics. Vol.29, No.11, November 1990, pp.L1977-L1980). Although it can be led that a band gap energy is used as an alternative of a kinetic energy, this reference does not teach or suggest values of kinetic energy of carriers to be considered and the degree of luminous intensity improvement is inadequate.
The inventor of the present invention conducted a series of experiments and, found that the suggested thicknesses of the first and the second layers by Takagi et al. were too small to confine electrons, and that preferable thickness of the first and second layers are 4 to 6 times larger than those suggested by Takagi et al.
Further, the present inventor thought that multiple quantum-wave reflection of carriers might occur by a multi-layer structure with different band width, like multiple light reflection by dielectric multi-film structure. And the inventor thought that it would be possible to confine carriers by the reflection of the quantum-wave. As a result, the inventors invented a preferable quantum-wave interference layer and applications of the same.
It is, therefore, a first object of the present invention to provide an LED in which an emission layer is sandwiched by quantum-wave interference layers with high reflectivity to carriers, functioning as reflecting layers. It is a second object of the present invention is to improve a luminous efficiency of an electron-hole pair by forming an emission layer sandwiched by quantum-wave interference layers in an LED having an emission layer in a p-layer.
In light of these objects a first aspect of the present invention is an LED constituted by two pairs of quantum-wave interference layers Each having plural periods of a pair of a first layer and a second layer as a unit. The second layer has a wider band gap than the first layer. The LED has at least a p-layer and an n-layer, and an emission layer is formed in the p-layer. The emission layer is sandwiched by two pairs of quantum-wave interference layers. Each thicknesses of the first and the second layers in the first quantum-wave interference layer is determined by multiplying by an odd number one fourth of a quantum-wave wavelength of electrons in each of the first and the second layers, and each thicknesses of the first and the second layers in the second quantum-wave interference layer is determined by multiplying by an odd number one fourth of a quantum-wave wavelength of holes in each of the first and the second layers.
The second aspect of the present invention is the LED constituted by the first and the second quantum-wave interference layers each having plural periods of a first layer and a second layer as a unit. Electrons which determine thicknesses of the first and the second layers formed in the first quantum-wave interference layer exists around the lowest energy level of the second layer.
The third aspect of the present invention is the LED constituted by the first and the second quantum-wave interference layers each having plural periods of a first layer and a second layer as a unit. Holes which determine thicknesses of the first and the second layers formed in the second quantum-wave interference layer exists around the lowest energy level of the second layer.
The fourth aspect of the present invention is to define each thicknesses of the first and the second layers in at least one of the first and the second quantum-wave interference layer as follows:
DW=nWxcexW/4=nWh/4[2mW(E+V)]xc2xdxe2x80x83xe2x80x83(1)
and
DB=nBxcexB/4=nBh/4(2mBE)xc2xdxe2x80x83xe2x80x83(2)
In Eqs. 1 and 2, h, mW, mB, E, V, and nW, nB represent a Plank""s constant, effective mass of carriers in the first layer, effective mass of carriers in the second layer, kinetic energy of carriers at the lowest energy level around the second layer, potential energy of the second layer to the first layer, and odd numbers, respectively.
The fifth aspect of the present invention is an LED having a plurality of partial quantum-wave interference layers Ik, formed in at least one of the first and the second quantum-wave interference layer, with arbitrary periods Tk including a first layer having a thickness of DWk and a second layer having a thickness of DBk and arranged in series. The thicknesses of the first and the second layers satisfy the formulas:
DWk=nWkxcexWk/4=nWkh/4[2mWk(Ek+V)]xc2xdxe2x80x83xe2x80x83(3)
and
DBk=nBkxcexBk/4=nBkh/4(2mBkEK)xc2xdxe2x80x83xe2x80x83(4)
In Eqs. 3 and 4, Ek, MWk, mBk, and nWk and nBk represent plural kinetic energy levels of carriers flowing into the second layer, effective mass of carriers with kinetic energy Ek+V in the first layer, effective mass of carriers with kinetic energy Ek in the second layer, and arbitrary odd numbers, respectively.
The plurality of the partial quantum-wave interference layers Ik are arranged in series from I1, to Ij, where j is a maximum number of k required to form a quantum-wave interference layer as a whole.
The sixth aspect of the present invention is an LED having a plurality of partial quantum-wave interference layers arranged in series with arbitrary periods, formed in at least one of the first and the second quantum-wave interference layer. Each of the plurality of partial quantum-wave interference layers is constructed with serial pairs of the first and second layers. The widths of the first and second layers of the serial pairs are represented by (DW1, DB1), . . . , (DWk, DBk), . . . , (DWj, DBj). (DWk, DBk) is a pair of widths of the first and second layers and is defined as Eqs. 3 and 4, respectively.
The seventh aspect of the present invention is to form a xcex4 layer between a first layer and a second layer which sharply varies the energy band and has a thickness substantially thinner than that of the first and the second layers, in at least one of the first and the second quantum-wave interference layer.
The eighth aspect of the present invention is to use at least one of the first and the second quantum-wave interference layer as a reflecting layer for reflecting carriers.
The ninth aspect of the present invention is to constitute a quantum-wave incident facet in at least one of the first and the quantum-wave interference layer by a second layer with enough thickness for preventing minority carriers from being injected into the first layer by a tunneling effect.
(First to Fourth Aspects of the Present Invention)
The principle of the quantum-wave interference layer of the present invention is explained hereinafter. First, the first quantum-wave interference layer, or an electron reflecting layer which reflects electrons, is explained.
FIG. 1 shows a conduction band of a multi-layer structure with plural periods of a first layer W and a second layer B as a unit. A band gap of the second layer B is wider than that of the first layer W. Electrons conduct from left to right as shown by an arrow in FIG. 1. Among the electrons, those existing around the bottom of the second layer B are likely to contribute to conduction. The electrons around the bottom of the second layer B has a kinetic energy E. Accordingly, the electrons in the first layer W have a kinetic energy E+V which is accelerated by potential energy V due to the band gap between the first layer W and the second layer B. In other words, electrons that move from the first layer W to the second layer B are decelerated by potential energy V and return to the original kinetic energy E in the second layer B. As explained above, kinetic energy of electrons in the conduction band is modulated by potential energy due to the multi-layer structure.
When thicknesses of the first layer W and the second layer B are equal to order of quantum-wave wavelength, electrons tend to have characteristics of a wave. The wave length of the electron quantum-wave is calculated by Eqs. 1 and 2 using kinetic energy of the electron. Further, defining the respective wave number vector in first layer W and second layer B as Kw and KB, reflectivity R of the wave is calculated by:
R=(|KW|xe2x88x92|KB|)/(|KW|+|KB|)
=[{mW(E+V)}xc2xdxe2x88x92(mBE)xc2xd]/[{mW(E+V)}xc2xd+(mBE)xc2xd]
=[1xe2x88x92{mBE/mW(E+V)}xc2xd]/[1+{mBE/mW(E+V)}xc2xd]xe2x80x83xe2x80x83(5).
Further, when mB=mW, the reflectivity R is calculated by:
xe2x80x83R=[1xe2x88x92{E/(E+V)}xc2xd]/[1+{E/(E+V)}xc2xd]xe2x80x83xe2x80x83(6).
When E/(E+V)=x, Eq. 6 is transformed into:
R=(1xe2x88x92xxc2xd)/(1+xxc2xd)xe2x80x83xe2x80x83(7).
The characteristic of the reflectivity R with respect to energy ratio x obtained by Eq. 7 is shown in FIG. 2.
When the second layer B and the first layer W have S periods, the reflectivity RS on the incident facet of a quantum-wave is calculated by:
RS=[(1xe2x88x92xS)/(1+xS)]2xe2x80x83xe2x80x83(8).
When the formula xxe2x89xa6{fraction (1/10)} is satisfied, Rxe2x89xa70.52. Accordingly, the relation between E and V is satisfied with:
Exe2x89xa6V/9xe2x80x83xe2x80x83(9)
Since the kinetic energy E of conducting electrons in the second layer B exists around the bottom of the conduction band, the relation of Eq. 9 is satisfied and the reflectivity R at the interface between the second layer B and the first layer W becomes 52% or more. Consequently, the multi-quantum well structure having two kinds of layers with different band gaps to each other enables effective quantum-wave reflection.
Further, utilizing the energy ratio x enables thickness ratio DB/DW of the second layer B to the first layer W to be obtained by:
DB/DW=[mW/(mBx)]xc2xdxe2x80x83xe2x80x83(10).
Thicknesses of the first layer W and the second layer B are determined for selectively reflecting either one of holes and electrons, because of a difference in potential energy between the valence and the conduction bands, and a difference in effective mass of holes and electrons in the first layer W and the second layer B. Namely, the optimum thickness for reflecting electrons is not optimum for reflecting holes. Eqs. 5-10 refer to a structure of the first quantum-wave interference layer for reflecting electrons selectively. The thickness for selectively reflecting electrons is designed based on a difference in potential energy of the conduction band and effective mass of electrons.
Further, the thickness for selectively reflecting holes is designed based on a difference in potential energy of the valence band and effective mass of holes, realizing the second quantum-wave interference layer for reflecting only holes and allowing electrons to pass through.
The electron reflecting layer and the hole reflecting layer as described above function as a p-cladding layer and an n-cladding layer, sandwiching an emission layer which is constituted by an i-layer, respectively. Accordingly, the LED according to the present invention having both the electron reflecting layer and the hole reflecting layer does not necessarily have the emission layer of a conventional LED, which is constituted by an i-layer sandwiched by an n-cladding layer and a p-cladding layer. As a result, the emission layer of the present LED can be constituted by a p-layer or an n-layer. Concerning that a mobility of holes is lower than that of electrons, it is effective to form an emission layer in a p-layer.
(Fifth Aspect of the Present Invention)
As shown in FIG. 3, a plurality of partial quantum-wave interference layers Ik may be formed corresponding to each of a plurality of kinetic energy levels Ek. Each of the partial quantum-wave interference layers Ik has Tk periods of a pair of a first layer W and a second layer B whose respective thicknesses (DWk, DBk) are determined by Eqs. 3 and 4. The plurality of the partial quantum-wave interference layer Ik is arranged in series with respect to the number k of kinetic energy levels Ek. That is, the quantum-wave interference layer is formed by a serial connection of I1, I2, . . . , and Ij. As shown in FIG. 3, electrons with each of the kinetic energy levels Ek are reflected by the corresponding partial quantum-wave interference layers Ik. Accordingly, electrons belonging to each of the kinetic energy levels from E1 to Ej are reflected effectively. By designing the intervals between the kinetic energies to be short, thicknesses of the first layer W and the second layer B (DWk, DBk) in each of the partial quantum-wave interference layers Ik vary continuously with respect to the value k.
(Sixth Aspect of the Present Invention)
As shown in FIG. 4, a plurality of partial quantum-wave interference layers may be formed with an arbitrary period. Each of the partial quantum-wave interference layers, I1, I2, . . . is made of serial pairs of the first layer W and the second layer B with widths (DWk, DBk) determined by Eqs. 3 and 4. That is, the partial quantum-wave interference layer, e.g., I1, is constructed with serial layers of width (DW1, DB1), (DW2, DB2), . . . , (DWj, DBj), as shown. A plurality I1, I2, . . . of layers such as layer I1 are connected in series to form the total quantum-wave interference layer. Accordingly, electrons of the plurality of kinetic energy levels Ek are reflected by each pair of layers in each partial quantum-wave interference layers. By designing the intervals between kinetic energies to be short, thicknesses of the pair of the first layer W and the second layer B (DWk, DBk) in a certain partial quantum-wave interference layer varies continuously with respect to the value k.
(Seventh Aspect of the Present Invention)
The seventh aspect of the present invention are directed forming a xcex4 layer at the interface between the first layer W and the second layer B. The xcex4 layer has a relatively thinner thickness than both of the first layer W and the second layer B and sharply varies an energy band. Reflectivity R of the interfaces is determined by Eq. 7. By forming the xcex4 layer, the potential energy V of an energy band becomes larger and the value x of Eq. 7 becomes smaller. Accordingly, the reflectivity R becomes larger.
Also, by sharply varying the band gap of the interfaces, the potential energy V of an energy band becomes larger substantially and the value x of Eq. 7 becomes smaller.
The reason why the reflectivity becomes larger can be considered as follows. Although the first layer W and the second layer B are formed so as to have the energy level as shown in FIG. 6A, actually some of the source gases to form one layer are mixed with other gases to form the other layer, when the layer to form is switched from one layer to the other. Then the energy level of the two layers does not change critically as shown in FIG. 6B. Accordingly, the first layer W and the second layer B, each having the different band width from that designed as in FIG. 6A, are formed. So, as shown in FIG. 6C, when a xcex4 layer which has a adequately thinner thickness than both of the first layer W and the second layer B and sharply varies an energy band is formed, the quantum-wave interference layer is considered to have the energy level as shown in FIG. 6D even if the source gases are mixed. Consequently, as illustrated in FIG. 6D, the energy level of the quantum-wave interference layer, in which a xcex4 layer is formed at the interface between the first layer W and the second layer B, can be close to the ideal energy level shown in FIG. 6A which is not obtained in the case of no xcex4 layer. Because the xcex4 layers shown in FIG. 6D are substantially thin, a tunnel conduction can be expected in the xcex4 layer. Although the xcex4 layer sharply varies the energy band, motion of carriers may hardly be affected by that.
Variations are shown in FIGS. 5A to 5D. The xcex4 layer may be formed on both ends of the every first layer W as shown in FIGS. 5A to 5C. In FIG. 5A, the xcex4 layers are formed so that an energy level higher than that of the second layer B may be formed. In FIG. 5B, the xcex4 layers are formed so that an energy level lower than that of the first layer W may be formed. In FIG. 5C, the xcex4 layers are formed so that the energy level higher than that of the second layer B and the energy level lower than that of the first layer W may be formed. As an alternative to each of the variations shown in FIGS. 5A to 5C, the xcex4 layer can be formed on one end of the every first layer W as shown in FIG. 5D.
Forming one xcex4 layer realizes large quantum-wave reflectivity at the interface between the first layer W and the second layer B. And forming a plurality of the xcex4 layers realizes a larger reflectivity as a whole.
(Eighth Aspect of the Present Invention)
The eighth aspect of the present invention is directed to a quantum-wave interference layer that functions as a reflecting layer and selectively confines carriers in the front of reflecting layer. As mentioned above, the quantum-wave interference layer can be designed to confine either electrons or holes selectively. Accordingly, by forming two kinds of quantum-wave interference layers each of which functions as an electron reflecting layer and a hole reflecting layer, respectively, both electrons and holes can be accumulated in the layer between the two kinds of the quantum-wave interference layers.
(Ninth Aspect of the Present Invention)
The ninth aspect of the present invention is to form a thick second layer B0 at the side of an incident plane of the quantum-wave interference layer, in order to prevent conduction by tunneling effects effectively and to reflect carriers.